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Review
Received: 30 September 2009 Revised: 12 February 2010 Accepted: 12 February 2010 Published online in Wiley Interscience: 7 April 2010
(www.interscience.wiley.com) DOI 10.1002/jctb.2387
Bioprocess scale-up: quest for the parameters
to be used as criterion to movefrom microreactors to lab-scaleMarco P. C. Marques,Joaquim M. S. Cabral and Pedro Fernandes
Abstract
Advancesin high-throughputprocessdevelopmentand optimizationinvolvethe rationaluse of miniaturizedstirredbioreactors,instrumented shaken flasks and microtiter plates. As expected, each one provides different levels of control and monitoring,requiring a compromise between data quantity and quality. Despite recent advances, traditional shaken flasks with nominalvolumes below 250 mL and microtiter plates are still widely used to assemble wide arrays of biotransformation/bioconversiondata, because of their simplicity and low cost. These tools are key assets for faster process development and optimization,
provided data are representative. Nonetheless, the design, development and implementation of bioprocesses can presentvariations depending on intrinsic characteristics of the overall process. For each particular process, an adequate andcomprehensive approach has to be established, which includes pinpointing key issues required to ensure proper scale-up. Recently, focus has been given to engineering characterization of systems in terms of mass transfer and hydrodynamics(through gaining insight into parameters such as kLa and P/V at shaken and microreactor scale), due to the widespread useof small-scale reactors in the early developmental stages of bioconversion/biotransfomation processes. Within this review,engineering parameters used as criteria for scaling-up fermentation/bioconversion processes are discussed. Particular focus ison thefeasibilityof the application of such parameters to small-scale devices and concomitant usefor scale-up. Illustrativecasestudies are presented.c 2010 Society of Chemical Industry
Keywords: scale-up; small-scale reactors; kLa; volumetric power consumption; fermentation; bioconversion
NOTATIONa Specific interfacial area (m1)
ai Initial specific surface area (m1)
af Final specific surface area (m1)
Bo Bond number, D2gWt1 ()
d Maximum inside shaking flask diameter (m)
D Well or vessel diameter (m)
di Diameter of drops in size class i(m)
Di Diffusivity (m2 s1)
dmax Maximum drop diameter (m)
dn Nozzle diameter (m)
do Shaking diameter (m)
d32 Sauter mean diameter (m)
Fr Froude number, do(2N)
2
(2g)
1
()g Gravitational constant (m s2)
h Liquid height (m)
k Number of size classes ()
kL Mass transfer coefficient (m s1)
kLa Volumetric oxygen mass transfer coefficient (s1)
N Shaking frequency, stirring speed (s1)
ni Number of drops ()
Nf Pumping number ()
NP Power number ()
P Gassed power input (W)
Po Ungassed power input (W)
P/V Volumetric power consumption (W m3)
Q Volumetric gas flow rate (m3 s1)
Re Reynolds number, Ndo21, NT21 ()Sc Schmidt number, (Di)
1 ()
T Stirrer diameter (m)
uo Nozzle velocity (m s1)
V Filling volume (m3)
vg Superficial gas velocity (m s1)
Vo Flask volume (m3)
vtip Impeller tip speed (m s1)
W Width of turbine blades (m)
We Weber number, N2T31 ()
Wt Wetting tension (N m1)
Subscripts
c continuous
T Tank
Greek symbols
Viscosity (Pa s)
Correspondence to: Marco P. C. Marques, IBB-Institute for Biotechnology andBioengineering, Centre for Biological and Chemical Engineering, Instituto
Superior T ecnico, Av. Rovisco Pais,1049-001 Lisboa, Portugal.E-mail: mpc.marques@ist.utl.pt
IBB-Institute for Biotechnology and Bioengineering, Centre for Biological and
Chemical Engineering, Instituto Superior T ecnico, Av. Rovisco Pais, 1049-001
Lisboa, Portugal
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Density (kg m3)
Local energy dissipation rate (W kg1)
Volume fraction of the dispersed phase ()
Interfacial tension (N m1)
V Viscous dissipation term (m2 s2)
INTRODUCTIONDespite sharing a common pattern, the design, development andimplementation of microbial processes present subtle variations,
depending on the product, microbial strain, growth conditions,
bioconversion/biotransformation conditions, among others. Thus,
for a given product, process or facility, an adequate and
comprehensive approach has to be established that encompasses
the detailed characterization of the process and the timely
identification of key process parameters likely to affect product
yield, quality and consistency. These are to be kept as constant
as possible throughout the scale-up process, in order to ensure
success of the later task.1,2
The development of microbial processes is strongly anchored
in small-scale reactors, typically Erlenmeyertype flasks and bench-
scale reactors, which are used for strain screening, media designand optimization and strategies of operation, ultimately aiming
for the highest attainable productivity.3 In recent years, the
range of small-scale vessels has increased to include multi-well
plates (MWPs) with different levels of complexity and built-in
devices, and miniature reactors that clearly emulate the larger
vessels, but with a volume in the milliliter (or lower) range4,5
Along with the technological developments that allowed for such
hardware, efforts have been made to ensure the data gathered
from experiments performed at these scales is reproducible
throughout scales. Such efforts have relied on gaining further
insight into mass (and heat) transfer and fluid dynamics at
microliter scale, identification and validation of key parameters
for scale-up, preferably from MWPs to bench-scale bioreactor,
and predictive modelling.6,7,8 Knowledge gathered allows fulladvantage to be taken of the high level of parallelization
provided by most miniaturized devices (in particular MWPs),
and to speed up bioprocess development in a cost-effective
manner.9,10,11 The task at hand is quite complex since there
are several parameters influencing transport phenomena and
chemical dynamics within a bioreactor. These parameters relate to
mass transfer, mixing, partitioning, power input, shear induced by
agitation, dilution rates, substrate and products concentration,
nutrients, micronutrients and stabilizing agents, temperature
and pH. Parameters of (bio)chemical nature are screened and
optimized for bioconversion/growth kinetics. Physical parameters
are, on the other hand, conditioned by process design and
operational conditions. The parameters for scale-up are selectedwithin the range of physical parameters. Naturally favored
candidates to fulfill such role are the process parameters
or coefficients that are known to have some effect on the
biological agent (enzyme or cell), particularly in their physiology.
These include those affecting oxygen supply, heat transfer and
mixing, namely aeration, agitation, mixing time, power input
and oxygen mass transfer coefficient.2,12 In many cases, these
physical parameters have to be combined with each other,
or with other variables, in dimensionless numbers that are
kept constant throughout scaling, therefore establishing scale-
up criteria. In any case, the environmental conditions have to
remain constant.1,2 Again, and despite the relevance of the
scale-up issue in biotechnology, there is no straightforward
and uniform strategy to tackle this matter. A suitable scale-up
approach has therefore to be established again on a casuistic
basis for a given product, process or facility.1,2,12 Most of these
strategies, when bioconversion, fermentation or cell culture
processes are involved, rely on the use of kLa or volumetric
power consumption as criteria for scale-up, although constant Re,
constant impeller tip speed and equal mixing and recirculation
time are occasionally used.2,13 Given the relevance of the
two former, they will be addressed in detail in this present
work.
SCALE-UP BASED ONKLAOxygen mass transfer coefficient
Oxygen is a key substrate in most microbial processes of industrial
relevance, where it can be required for growth, maintenance
or production of metabolites.14,15 These processes are typically
performed in an aqueous environment, but oxygen is sparingly
soluble in water, roughly 0.272 mmol L1, at 25
C and 101 kPa
air pressure, and thus often becomes the limiting substrate.16 A
suitable supply of oxygen to the liquid media, typically from air,
is mandatory, but the process of mass transfer is influenced byseveral variables,such as physical properties of the fluids involved,
operational conditions and geometry of the reactor. The oxygen
transfer rate (OTR) can be increased by altering stirring speed and
gas flow, which concomitantly alters the power input. Increasing
the OTR is required to cope with the microbial oxygen demand,
the oxygen uptake rate (OUR). It is possible to assess the rate
limiting step of a microbial process, i.e. mass transfer or reaction
limited, through the use of a modified Damkohler number (Da),
which is calculated as the ratio between the maximum oxygen
uptake and transfer rates.17
Da =OURmax
OTRmax(1)
A large qO2 or low diffusivity leads to Da > 1, hence the
process is mass transfer limited; oppositely, small qO2 or high
diffusivity results in Da 1, thus the process is limited by the
biochemical reaction rate.18 Oxygen transfer rate is thus a critical
feature for the characterization of a given process and likewise
an engineering parameter suitable for the design, selection and
scale-up of bioreactors is to address OTR. One such parameter
is the volumetric mass transfer coefficient kLa, which relates the
oxygen mass transfer rate to the oxygen concentration gradient,
according to (2). In a bioprocess the oxygen mass transfer rate can
be described by12,16
OTRC CL
= kLa (2)where OTR is expressed as the molar flux of oxygen through the
gasliquid interface; C is the dissolved oxygen concentration
which would be in equilibrium with the gas phase, CL is the
dissolved oxygen concentration in the bulk liquid, kL is the
local mass transfer coefficient in the liquid phase, and a is the
specific interfacial area. Although oxygen is transferred from the
bulk gas phase to the bulk liquid phase, it is assumed that
the gas phase resistance to mass transfer is negligible. Oxygen
consumption through the process due to biochemical reactions
can be considered using a biological enhancement factor, E,13,18
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leading to an overall volumetric mass transfer coefficient KLa given
by
KLa = E.kLa (3)
E incorporates the transport enhancement due to the oxygen
uptake by microorganisms, alongside with opposing mass
transfer resistances caused by layers of materials placed between
the gas bubble and the bulk liquid phase, namely adsorbed
surfactant and cells, and stagnant liquid film.18,19
E has beenshown experimentally to change with the concentration of
biomass, typically increasing with increased cell concentration,
but with varying patterns, according to different strains and
incubation media. In these dedicated experiments, E was within
0.81.3, although values as high as 5 were also reported.13,18,19
Nonetheless, and for most cases, the biochemical rate is not
significantly larger than the mass transfer rate, hence it is usually
assumed that E= 1. Details on this matter can be found in the
recent review by Garcia-Ochoa and Gomez.13
The volumetric mass transfer coefficient in bioreactors can be
obtained experimentally or predicted using empirical correlations
for kLa, or for kL and a, which are thoroughly described
elsewhere,13 coupled to a model for the estimation of E. The
introduction of the latter parameter in predictive determinationshas nevertheless been seldom reported, which may account for
shifts between predicted and experimental data at high biomass
concentrations. The use of constant kLa as scaling criterion is
widely disseminated in conventional scales, from laboratory to
production scales, encompassing volumes ranging from 1 L to
1000 m3, and ultimately has also been found to be suitable down
to the milli/micro-liter scale.68,2025
Experimental determination of the volumetric mass transfercoefficient (kLa)
Several methods have been developed to determine kLa
experimentally.13,26,27 Within the scope of bioreactor design,
several items are considered: stoichiometry, thermodynamics,microbial kinetics, transport phenomena (heat and mass transfer)
and economics. While the first three items are scale-independent,
transport phenomena and economics are extremely dependent
on scale. The relevance of the transport phenomena in the design
and scale-up of the bioreactor is particularly noticeable, since the
overall rateof aerobic bioprocesses is generally controlled by mass
transfer rates. The mass balance for the dissolved oxygen in the
well-mixed liquid phase can be established as2,12,13,16
dC
dt= OTR OUR (4)
where dC/dt is the oxygen accumulation rate in the liquid phase.
The determination of OTR can be performed either when oxygenis being depleted by growing biomass (direct methods) or when
no oxygen uptaketakesplace (indirectmethods).In thelatter case,
equation (4) reduces to
dC
dt= OTR = kLa
C C
(5)
The direct methods rely on oxygen probes, which allow for
the determination of OTR through gas phase analysis or through
the dynamic method. Until recently, only relatively bulky probes
were available, which prevented oxygen monitoring in miniature
vessels (MWPs, miniature/micro bioreactors), limiting its use to
bench scale and larger bioreactors. Recently Erlenmeyer-type
shaken flasks were adapted in order to be equipped with oxygen
gas sensors, allowing for on-line determination of OTR in several
parallel experiments in shaken vessels.28,29,30 Developments in
fluorescence methods, (micro)fabrication techniques and optic
fiber, have allowed for the implementation of sensitive dyes that
can either be inserted into a patch and adhered inside a vessel,
including individual wells from multiwall plates, yielding the so-
called sensor spots, or incorporated onto the tip of fiber optic
probes.3,4,11,25,31 37
The indirect approach for the determination of OTR relies on
chemical or physical methods. The most commonly used among
the former is the cobalt-catalyzed oxidation of sulfite, which was
optimized for application in miniature bioreactors (MWPs and
shaken flasks),38 and is routinely used in such formats.33,39 A
methodbasedonCO2 absorption is morerarely used.The physical
methods, again relying on probes, allow for the dynamic method
of OTR determination.13 Chemical methods, and in particular
the sulfite method, may be biased due to modifications in fluid
dynamics, fluid properties and surface tension, as a result of the
addition of chemicals. They may therefore lead to misleading
information and data gathered.13,27,40,41The use of fast enzymatic
methods has also recently been introduced within the scope ofthe indirect approach. These are clearly designed for application
in miniature systems, such as MWPs.42,43 These methods are
based on the use of glucose oxidase and, preferably, of catechol
2,3-dioxygenase. The latter method relies on a single-step well
defined stoichiometric reaction, whereas the former requires
calibration with the sulfite method (or a similar one) but on
the other hand, all reagents are easily available. Among physical
methods, the dynamic method is the most commonly used to
evaluate kLa, because of its simplicity and relative accuracy. Both
the absorption and desorption measurements give equal values
of kLa under identical hydrodynamics conditions.44 When the
characteristic time for the oxygen electrode and the characteristic
time for the oxygen transfer process (1/kLa) are of the same
magnitude, the dynamic response of the electrode has to beconsidered in the determination of kLa. A detailed description
on the nature and limitations of the methods used for the
experimental determination ofkLa is given by Garcia-Ochoa and
Gomez.13
Empirical correlations for the determination ofkLa in stirredtank reactors
Both dimensional and dimensionless equations for the volumetric
mass transfer coefficient as functions of different variables have
been proposed.45 There are, however, considerable problems
concerning the accuracy ofkLa estimation. Discrepancies between
experimental data and those estimated from these equations are
often found. The discrepancies are mainly found when kLa forreal broths are estimated from equations proposed for aqueous
solutions. This can be due to the strong influence of the type and
sizeof thebioreactor,the differentrangeof operational conditions,
the system considered (solutions or real broths), or even the
measuring method used.46,47 The addition of ions, hydrocarbons
or temperature increase kLa, whereas the addition of surfactants
or antifoams or increases in media viscosity decrease kLa, when
compared with data obtained from water.26,4852
Vant Riet26 proposed an overall correlation of kLa with
volumetric power consumption and superficial gas velocity:
kLa = C1 P
VC2
vgC3 (6)
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where P is the gassed power input, V is the liquid volume, vgthe gas superficial velocity and C1, C2 and C3 are constants that
may vary considerably. Weuster-Botz etal.53 used correlation (6)
to predict kLa in a magnetically driven stirred column, designed for
parallel operation in an incubator chamber, operated as shaking
flasks. Constants varied from 0.11 to 0.14, 0.06 to 0.37 and 0.73 to
0.22, for C1, C2 and C3, respectively, according to differentturbines.
Mass transfer coefficients of up to 0.34 0.05 s1 were obtained
in the reactors, using defined medium for growing E. coli, using
the dynamic gassing-out method.
Montes etal.54 determined values of kLa in yeast broths
(Trigonopsis variabilis) over wide ranges of both impeller speeds
and superficial gas velocities, in three different mechanically-
stirred, baffled reactors (2, 5 and 15 L). Experimental data were
fitted using Equation (6) and the values for the parameters C2, C3and C1 were 0.35, 0.41 and 3.2 10
3, respectively. Since most
of the yeast broths behave as non-coalescent fluid, according to
the authors, the correlation improved the prediction ofkLa values
with respect to other generic correlations usually developed for
strong coalescent and non-coalescent fluids. Additionally, Shin
etal.55 verified that in high cell density cultures of fast-growing
aerobes, such as recombinant E. coli, where the biomass mayincrease to more than 70 gL1, the oxygen availability can be the
rate-limiting step of the fermentation process. Accordingly, the
following correlation for kLa incorporating the effect of cell density
(X) in oxygen transfer has been proposed:
kLa = 0.0192
P
V
0.55 vg0.64
1+ 2.12X+ 0.2X20.25
(7)
Extensive details on this matter can be found elsewhere.13
Another approach for the estimation of kLa relies on the use
of empirical correlations incorporating dimensionless groups.13,45
This approach has certain advantages because the correlations
obtained for a known system can be used to estimate kLa in other
systems with different dimensions.5658
Although several correlationshave beendevelopedfor different
systems, most of them are not specific to fermentation broths or,
when developed with such a purpose, they do not take into
consideration all the variations of parameters (surface tension,
viscosity) throughout the time course of cultivation, which may
hamper its effectiveness.
Two-phase partitioning bioreactors have demonstrated signif-
icant potential for enhancing the productivity of many biopro-
cesses by overcoming issues of poor substrate solubility and
toxicity. The oxygen mass transfer coefficient can also be evalu-
ated in these systems. In order to take into account the effect of
the organic phase and the organic phase volume fraction on kLa
in aerated liquidliquid dispersions, empirical correlations havebeen proposed, assuming that the two liquid phases behave as a
single homogeneous phase:59
kLa =
P
V
vg
(1 ) (8)
where is the volume fraction of the dispersed liquid phase, and
, , and are numerical constants.
Gomes etal.60 applied the correlation to the biotransformation
of methyl ricinoleate into -decalactone by the yeast Yarrowia
lipolytica. They showed that kLa had an influence on the
aroma production; however, for the low hydrophobic substrate
concentration used (1.08% v/v) and cellular density of 2 .0 107
cells mL1, a minimal kLa value of 70 h1 was necessary to attain
the maximum aroma production, 141 21 mg L1 (obtained at
agitation andaeration rates of 400 rpmand 0.6 vvm, respectively).
The numerical constants used were 650, 0.3, 0.7 and 1.7, for , ,
and , respectively.
Hydrodynamic studies in two-phase partitioning bioreactors
have focused on gaining further insight into understanding the
mechanismsrelatedwith formation of the interfacial areaavailable
formass transfer, so that substrate supply (normally from the non-aqueous phase) does not become the rate limiting step of the
process. The interfacial area has previously been correlated with
the dispersed phase hold-up fraction and the Weber number.61
The interfacial area available for mass transfer (a) is given by
a =6
d32(9)
where d32 is the Sauter mean drop diameter. Accurate knowledge
of the effectof bioreactor operating conditions on d32 is therefore
very important. Knowledge ofd32 can also give an early indication
of the stability of the liquidliquid dispersion created. The
physicochemical properties of the media can influence both
mean drop size and drop size distribution, as observed by Torres-Martinez, in the characterization of a multiphase system involving
ionic liquids.62
kLa determination in shaken devices
One of the key challenges for shaken fermentation technology
is to provide sufficient oxygen for the optimal growth of aerobic
microorganisms.63 Adequate oxygen supply is crucial not only
for industrial production, but also for meaningful screening and
processdevelopment.64 Underoxygen-limitingconditionsaerobic
microbes grow slowly, production of the intended metabolites is
scarce, if any, and furthermore, unwanted synthesis of metabolites
typical of anoxic conditions is prone to occur. Results obtained
under such conditions are likely to be misleading, particularly forscale-up purposes.63 To study the effect of organism properties,
medium composition or cultivation strategy on growth and
production, incubation in a non-limiting oxygen environment
is absolutely necessary. Otherwise wrong information about the
variables under study might be obtained.65,66
Several operational parameters affect the OTR in shaking
devices, namely the shape and size of the vessel; the shaking
frequency; the shaking amplitude; the shaking angle; the type
of agitation (orbital or linear); and the filling volume. OTR is
also influenced by the surface properties of the flask material,
which may be either hydrophobic or hydrophilic; and by the
physical chemical properties of the liquid (viscosity, oxygen
solubility, diffusivity and surface tension, the latter being more
noticeable in MWP).3,27,67
Some particular setbacks are likely to occur when operating
shaken vessels, specifically:
1. The reproducibility of microbial growth might be poor.68
2. When baffled vessels are used, small differences in depth
and positioning of the baffles lead to significant differences
in oxygen supply, growth and product formation of parallel
cultivations.
3. Out-of-phase phenomena might occur.67
4. Shaking frequency in these flasks has to be reduced to avoid
splashing of the liquid. Were droplets to reach the plug of
the flasks, gas transfer limitations or contaminations might
occur.63
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Engineering features and correlations forkLa in shaken flasksand MWP
Since bioprocess development (strain selection, strain enhance-
ment,process optimization) is widely carried out in shakenvessels,
and efforts towards engineering characterization of the oxygen
transfer mechanisms in such devices have been undertaken.
Maier and Buchs determined the maximum gasliquid mass
transfer capacity in 250 mL shaking flasks on orbital shaking
machines, using the sulfite oxidation method, by variation of
the shaking frequency and diameter, filling volume and viscosity
of the medium. The distribution of the liquid within the flask
was modeled, taking as reference the intersection between the
rotational hyperboloid of the liquid and the inner wall of the
shaking flask.69
The mass transfer within the shake flask is conditioned by
two resistances: one due to the sterile closure of the vessel, the
other due to the gasliquid interface. Owing to the resistance of
the closure, the oxygen partial pressure within the flask is lower
than the oxygen partial pressure of the surroundings. Mrotzek
etal.70 concludedthat, under normal conditions, the mass transfer
resistance of sterile closures is far smaller than the resistance of
the gasliquid interface.The gas exchange through the sterile closure was described
by the extended model of Henzler and Schedel,71 where besides
Fick diffusion flow, other parameters and issues are taken into
consideration, such as: (i) gas transfer by combined action of
diffusion and convection due to non-equimolar mass exchange
(Stefan flow); (ii) diffusion coefficients are notregardedas constant
but are instead calculated as a function of the respective local gas
concentration; and (iii) consideration of the water vapor flow.
Operating with baffled flasks, and using suitable operating
conditions, such as large shaken amplitudes, high OTRs can be
obtained. In 250 mLshaking flasks witha filling volume of50 mL, a
kLa of 400 h1 was obtained with a shaking amplitude of 2.5 cm. If
theamplitude wasincreased to 5 cm,similar valueswere obtained
at lower shaking frequencies. In these cases, the resistance of thesterile closure can become the limiting factor.
Experimental data from given sets of experiments were fitted
by least-squares after dimensional analysis,67 and the following
proportionality for the maximum oxygen transfer capacity
(OTRmax) was found
OTRmax N0.84V0.84d0
0.27d1.25 (10)
Consequently, an increase of the maximum oxygen transfer
capacity of a given system can be achieved by increasing the
shaking frequency, reducing the filling volume, increasing the
shaking diameter (d0) or reducing the maximum flask diameter (d)
(this is only valid when the V1/3
/dratio remains constant).Taking this into account, Maier etal.72 modeled the gas liquid
mass transfer in shake flasks at water-like liquid viscosity, in flask
sizes between 50 and 1000 mL. Relative filling volumes of 4 16%,
shaking diameters of 1.25, 2.5, 5, 7, 10 cm andshaking frequencies
of 50 500 rpm were tested. Furthermore, the previous model of
the gasliquid mass transferEquation (10)was extended to a two
sub-reactor model, to account for different mechanisms of mass
transfer in the liquid film on the flask wall, and the bulk of the
liquid rotating within the flask. The two-reactor system approach
consists of a stirred tank reactor (bulk liquid) and a film reactor
(film on flask wall and base). The mass transfer into the film on the
flask wall and base at in-phase operating conditions, is described
by Higbie penetration theory. Two differentmass transfer theories
were applied to successfully describe the mass transfer into the
bulk liquid: a model by Kawase and Moo-Young73 and a model by
Gnielinski.74 Extensive details can be found elsewhere.72
The agreement between the new modeling approach and the
experimental data was within 30%. The applicability of the
latter models to a biological system was shown using a Pichia
pastoris culture. The OTRmax was determined using the sodium
sulfite method which displayed a correlation factor of 2.8, when
compared with the OTR determined using an oxygen limited
P. pastoris culture, under variation of the operating conditions
(250 mL shake flask with filling volumes of 15, 25 and 40 mL,
under shaking frequencies of 50500 rpm with 5 cm of shaking
diameter).72 Moreover, the volumetric mass transfer coefficient
models allowed a significant agreement between experimental
dataandmodelpredictions,asreflectedbyacorrelationcoefficient
of 0.88. The maximum volumetric mass transfer coefficient of the
experimental investigation was found to be 0.157 s1 inthe 50 mL
flask, at a relative filling volume of 4%, a shaking frequency of
450 rpm and a shaking diameter of 7 cm.
Liu etal. correlated the experimental data for the determination
of OTR with a multivariable power correlation in carotenoid
(astaxanthin) production by the red yeast Phaffia rhodozyma.15
The constant parameters were derived by linear regression of the
data, resulting in the following equation:
kLa = 0.141N0.88
V
V0
0.80(11)
where Vo is the flask volume. Results showed a direct linear
correlation between carotenoid yield and OTR (OTR from 0 to
690 mg L1 h1), indicating that carotenoid production is limited
by oxygen transfer. Mantzouridou etal.75 also investigated the
effect of oxygen transfer rate on -carotene production by
Blakelsea trispora in shake flasks. The results indicated that the
concentration of-carotene (704.1 mg L1) was highest in culture
grown at maximum OTR of 20.5 mmol L1 h1. Moreover, OTRlevelshigher than20.5 mmol.L1h1 werefound to be detrimental
to cell growth and pigment formation.
Besides increasing the diameter or frequency of shaking or
decreasing the filling volume, one possibility to achieve high
maximum oxygen transfer capacities (OTRmax) is to modify the
usual round geometry of the shaken vessel. As shown by many
groups, changing the geometry of the vessel (i.e. from round-
bottomed base to square-bottomed base) and/or introducing
baffles into shake flasks resultin a significant increase in maximum
oxygen transfer capacity.76 The OTRmax can be increased up to
5 10-fold even at low shaking frequencies.
Alternatives for the well bottom design have been established,
among them the square shaped well. This type of well geometryhas been investigated by Duetz and Witholt42,77 and Duetz etal.78
The effects found for square wells are comparable with those in
baffledshake flasks.Eventhough squarewells allowfor an increase
in OTRmax of roughly 100% when compared with round wells, the
aforementioned problems described for shake flasks (splashing
and out-of phase phenomena) may limit the utilization of square
deep well plates as cultivation vessels.
More recently, Funke etal.79 presented well configurations with
a geometry thataimed at avoiding splashing while simultaneously
allowing for a high filling volume. Different plate formats were
studied, where variation were achieved by increasing the number
of edges and rounding the edges in square geometry plates,
rounding edges in pentagonal shape wells, star and flower
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shape wells, among others. Dissolved oxygen tension (DOT) was
measured in an experimental setup described by Samorski etal.80
The well geometry proved influential for OTRmax. By introducing
such baffles, an OTRmax in excess of 100 mmol L1 h1 (kLa over
600 h1) was obtained, roughly double that of round 48-well
MWPs. In conventional MWPs, values for OTRmax reported so far
have not generally exceeded 50 mmol L1 h1.27 Values of the
OTR in stirred tank reactors can reach 500 mmol L1 h1, but
overall, in standard batch fermentations, the OTR does notexceed
100 mmol L1 h1.26 The final well design, a six-petaled format,
provided the best compromise among different levels of baffling,
allowing simultaneously for a stable liquid height at the well
center during shaking (strong), high OTRmax independently of
filling volume and shaking frequency (moderate), and high filling
volume without splashing.79
Nonetheless, there are two common problems associated with
the use of microtiter plates for carrying out fermentations. These
are evaporation and cross-contamination due to spillover.In order
to avoid these drawbacks, MWPs can be sealed with adhesive
tape. The use of sealing tape leads to airtight closure of the wells
decreasing oxygen transferto the reactor welland consequentially
to the reaction medium.11
Doig etal.81 modeled the volumetric oxygen transfer coefficient
in MWPs using dimensionless groups. The basis for the modeling
was the experimental measurements of airliquid specific surface
area, determined both by the rate of evaporation and by high-
speed video photography.
Flowbehaviorwas modeled separatelyaccording to the specific
microplate configuration (24, 96 and 384-well), and the following
correlations, respectively, were obtained:
af
ai= 2.895 Fr0.86Bo0.03 (12)
af
ai= 1.092 Fr0.64Bo0.15 (13)
af
ai= 0.607 Fr0.51Bo0.18 (14)
The different models for predicting specific air liquid surface
area (af/ai) converged, with most data points lying within 25%
of the predicted values.
The kLa values ranged from about 0.005 to 0.055 s1 (shaking
amplitude of 3 mm and shaking frequencies ranging from 200
to 800 rpm) and are within the range reported by other authors
for these devices.5,35,78,82 Since the specific surface air liquid area
increased by a maximum factor of 4, and kLa increased by up to
10, it is clear that the liquid side oxygen transfer coefficient kL was
also affected by shaking conditions. Hermann etal.82 observed
an increase in kL from about 5.5 10
5
to 1.4 10
4
ms
1
asshaking frequency was increased from 200 to 800 rpm at 25 mm
amplitude. Values calculated by Doig etal.81 for kL varied from
2.8 105 ms1 to 8.3105 ms1 (shaking amplitudes of 3 mm
to 8 mm, in 24, 96 and 384 well microtiter plates).
Correlations for kL typically encompass Reynolds and Schmidt
numbers,and areusuallyin theformSh = a RebScc,where b ranges
from 0.7 to 0.8 and c is usually 0.33.81 The optimized correlation
for all three microplate geometries is
Sh = 0.19 Re0.68 Sc0.36 (15)
All the experimental data were modeled within 30% de-
viation, using correlation (15). Combining equation (15) with
Equations (12)(14), an overall correlation for predicting the vol-
umetric oxygen transfer coefficient kLa, in round bottom plates
becomes
kLa = 31.35DiaiRe0.68 Sc0.36 FrxBoy (16)
where Di is the diffusion coefficient, ai is the initial specific surface
area, and x and y are constants depending on the microplate
geometry (according to Equations (12)(14).
Islam etal.83
modified Equation (16) in order to predict kLa insquare well microtiter plates. The correlation obtained was:
kLa = 3.94 104
T
D
ai Re
1.91eaFrb
(17)
where the values for a and b were 1.66 and2.47 for48 rectangular,
flat wells; 0.70 and 1.51 for 24 square wells, round bases; and 0.88
and 1.24 for square wells, pyramidal bases. The predicted values
were in good agreement with the experimental data for kLa.
Case studies: scale-up from shaken devices and miniaturestirred reactors based inkLa similarity
In previous studies84 kLa was identified as the key engineering
parameter for characterization of an E. coli based process forheterologous protein expression, in microtiter plate format. A
scale-up to 7.5 and 75 L stirred tanks was performed, using as
criterion kLa fixed at either 0.069 s1 or at 0.015 s1. At 0.069 s1
boththe fermentation profile (biomass concentrationand glycerol
consumption) and product yield were identical in all scales,
enabling a 15 000-fold quantitative scale-up, representative of
fermentation performance. At 0.015 s1, due to poor gasliquid
distributions observed within the larger stirred tanks at matched
kLa, the overall fermentation profile was not reproduced.
Micheletti etal.6 studied the scale-up of aerobic fermentation
of E. coli JM107:pQR706 for overexpressing transketolase (TK),
from microtiter plates to stirred reactors. Using the correlation
displayed in Equation (17), a kLa of 0.079 s1 at 1000 rpm for
a 96 deep well microtiter plate was obtained. Maintaining the
volumetric oxygen mass transfer coefficient, it was possible to
scale-up the process directly from the microwell reactor to a lab-
scale reactor (1.4 L). Apart from some differences in duration of the
lag phase observed when the two scales were compared, similar
values ofmax and final biomass concentration were obtained.
Likewise, the rates of L-erythrulose formation when the cells
from the respective fermentations were used for the subsequent
HPA(-hydroxypyruvate) and GA (glycolaldehyde) bioconversion,
were also similar.
Zhang etal.8 used computational fluid dynamics (CFD) to
provide a detailed characterization of fluid mixing, energy
dissipation rate and mass transfer in single well bioreactors,
from deep square 24-well and 96-well microtiter plates. The CFDsimulations showedthat liquidmixing is more intensive in 96-well
than in 24-well bioreactors, due to the vertical movement of the
bulk fluid, in addition to the rotational movement. Liquid motion
was strongly dependent on the orbital shaking amplitude which
generally has a greater impact than the shaking frequency.
Predicted kLa values were compared with experimental results
obtained from dynamic gassing out experiments using a fibre-
optic dissolved-oxygen probe. The resulting kLa values measured
were 0.036 s1 and 0.023 s1, at 1000 rpm and 500 rpm, respec-
tively, in 96-well MWPs, at an orbital shaking amplitude of 3 mm.
The corresponding predictedvalues, 0.065 s1 and 0.056 s1 ,were
higher. The discrepancy was ascribed to some features of the dy-
namicmethod,namelytotheprobesensitivitytowardstheshaking
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movement of the microtiter plates, as well as to the positioning of
the probe andto the mixingtime. CFDstudies could give more ac-
curate values if mediumlosses due to evaporation were taken into
account, and if the actual physical properties of the fermentation
media (viscosity, density) were used instead of water, as input for
performing the calculation. Batch cultures ofE. coliDH5 showed
similar maximum specific growth rates and final biomass yields
in shaken 24-well MTP and Erlenmeyer bioreactors, and in stirred
miniature and 20 L bioreactors at matched kLa values.
The biotransformation of benzaldehyde to l-phenyl acetyl
carbinol was scaled-up from a 100 mL shake flask to a 5 L reactor,
using resting cells of Saccharomyces cerevisiae.85 The following
correlations were used for the prediction of kLa in the growth
medium and in the biotransformation medium, respectively,
kLa = 0.024
P
V
0.725v0.892g (18)
kLa = 6.99 106
P
V
1.14v0.365g (19)
The volumetric oxygen mass transfer coefficient varied from0.010.07 s1 in the growth medium to 0.0050.02 s1 in the
biotransformation medium. Maintaining the kLa constant as
scale-up criteria, both for the cell growth process and for the
biotransformation, a 50-fold scale-up was achieved.
Gill etal.7,86 studied the influence of kLa on the fermentation
of E. coli TOP10 pQR239 in a 100 mL reactor. A correlation was
developed for the miniature reactor
kLa = 0.224
P
V
0.35v0.52g (20)
which was validated using the dynamic gassing out technique.
For scale-up to a 2 L bioreactor, different values of kLa were
used, varying from 0.06 to 0.11 s1. The results showed that therewas good agreement between cell growth and dissolved oxygen
tension profiles across the range ofkLa values studied, compared
with experiments at matched P/V values. The trend in oxygen
depletion during the growth phase and the time taken for both
systems to become oxygen limited were similar and reproducible
in both cases, thus resulting in a satisfactory 20-fold scale-up.
Using an E. coli JM107:pQR706 overexpressing transketolase
system, Micheletti etal.6 showed that kLa is the most suitable
scale-up parameter from a 24-well microtiter plate (1 mL filling
volume) to a 2L stirred tank reactor. On the other hand, the
prediction for the power consumption in the mechanically stirred
bioreactor (3.64 W m3) working under operational conditions
that allowed for growth patterns that matched those in shakenvessels was roughly 10-fold lower.
More recently, Marques etal.5 achieved an 8000-fold scale-up
for the side-chain cleavage of -sitosterol performed by whole
cells of Mycobacterium sp. NRRL B-3805 in 24-well microtiter
plates to a 5 L reactor. Scale-up was performed based on kLa
similarity at 0.058 s1 (at a shaking frequency of 250 rpm and
filling volume of 0.5 mL). Similar profiles (glycerol consumption
and 4-androstene-3,17-dione (AD) production) were achieved in
both scales validating multi-well plates as a small-scale reactor
for performing complex bioconversions. Nonetheless, there was
a consistent gap between values obtained in the multi-well
plate system and the bench-scale reactor for AD production and
biomass formation visible also in the levels of oxygen depletion.
The behavior was ascribed to diverse intrinsic hydrodynamic
conditions in the different reactor configurations, since mass
transfer plays an important role, both for oxygen and substrate
uptake.
Both MWP as well as miniature bioreactors proved effec-
tive as starting platforms for scaling up to bench/pilot scale
biotransformation/fermentation, but further studies in different
environments would be welcome that would hopefully further
validate this approach. Case studies are relatively scarce, where
miniature bioreactors are concerned. This can be partly ascribed
to the wider dissemination and lower cost of MWP platforms,
when compared with miniature bioreactors, whose availability in
the market is clearly lower.11 The studies referred to in this paper
related to the use of miniature bioreactors are based on in-house
developed prototypes. The use of the simpler MWPplatforms may
be of limited use when pH shifts take place during the process,
given the lack of mechanisms for pH control, only available in
more complex platforms.11 Processes involving significant shifts
in broth rheology (i.e. production of polymers) or viscous envi-
ronments may be more adequately dealt with using miniature
bioreactors, since these may provide more efficient mixing.
SCALE-UP BASED ON VOLUMETRIC POWERCONSUMPTIONPower consumption is a key parameter in (bio)chemical engineer-
ing,i.e. anengineering characterization parameter. Concomitantly,
it is a strong candidate for use as a criterion for (bio)reactor de-
sign and process scale-up. Often referred to as volumetric power
consumption (P/V), it is defined as the amount of energy required
to generate movement of a fluid within a vessel in a given pe-
riod of time. Along with the power actually drawn by the fluid,
relevant to the outcome of a given process, further power is re-
quired to account for energy losses, mostly due to friction, and
power consumption by motorsand gearboxes. This excess power,
although often relevant in terms of overall power consumption,
is not considered for design or scale-up of the process. The vol-
umetric power consumption is representative of the turbulence
degree and media circulation in vessels, and influences heat and
mass transfer, mixing and circulation times.87 Constant volumetric
power input wasapplied successfully as scale-up parameterfor the
early industrial penicillin fermentations (1 hp gallon1, equivalent
to1.8 kW m3), andin fermentations with lowenergy inputs,88 but
it is limited in fermentations requiring high energy inputs, such
as recombinant E. coli cultures,1 possibly due to high associated
costs and to high shear stress in the larger-scale stirred vessels.
AccordingtoRushton etal.,89,90 thepowerinputfortheagitation
of a non-aerated mixture, Po is characterized by the dimensionless
variable power number (NP):
P0 = Np N3T5 (21)
where N is the stirrer speed and T the stirrer diameter. The
power number depends on other dimensionless groups such as
Reynolds number and Froude number, as well as on the number
of agitator turbines. Thepowerconsumption in ungassed systems
is always higher than the power consumption in gassed systems,
since aeration significantly influences the power drawn from the
impeller by the fluid.7 The effect of aeration has been studied
extensively by Nienow etal.,91 Oosterhuis and Kossen,92 Yawalkar
etal.93 and Gogate etal.46 It has been shown that the gassed
power input is usually 3040% of the ungassed power input,
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depending on the type of impeller and aeration rates used.79
Cavities (gas pockets) are formed behind the impeller blades in
gassed systems, resulting in different densities of the fluid under
gassed and ungassed conditions.94,95 Too high gas flow is to be
avoided since this may lead to cavities extending between blades,
which result in flooding and mechanical instability. Cavities may
be minimized,hence gas handling capacityimproved, withthe use
of adequate impellers, such as the Rushton turbine. Alternative
blade impeller configurations (i.e. concave blades) have also been
introduced.96,97
Hughmark98 suggests the following relationship for estimating
the volumetric power consumption:
P
Po= 0.1
N2T4
gWV23
1
6 Q
NV
14
(22)
where W is the width of turbine blades and Q is the volumetric
gas flow rate. Over the years several modification were proposed
in order to improve this model. Such modifications included
taking into account the number and type of impellers and reactor
dimensions, among others.99,100,101
Along with the use of predictive correlations, power con-
sumption may be determined experimentally through the use
of electrical or calorimetric measurements, or through the use of
dynamometers, torquemeters and strain gauges.87
In bench- and pilot-scale bioreactors typically used for the
fermentation of bacteria and fungal micro-organisms, the power
consumption ranges from 1 to 3 kW m3.102,103
Shaken flasks
Although well established for bench-scale and above reactors,
only recently have dedicated efforts been made to provide a
suitable characterization of the volumetric power consumption in
miniaturized devices, and to take advantage of this parameter forthe engineering characterization of said devices. Most reports on
the experimental determination of power consumption in shaking
systems are by the group of Jochen Buchs at RWTH Aachen. Buchs
etal.104,105 measured the power consumption in shaken flasks at
high and low-medium viscosities. The experimental assembly was
a simplerotary shaking machine fixed to a frame,combinedwith a
torque sensorattached tothe powering drive.Torque andshaking
speed were monitored and correlated by the following relation:
P
V= Ne
N3d4
V23
= C3N3d4
V23
Re0.2 (23)
where Ne
is the modified Newton number for shake flasks.The correlation implies that the specific power consumption is
dependent on the shaking frequency according to P N2.8. Such
a correlation is typical of that found in unbaffled agitated tank
reactors. The model includes C3 as the only fitting parameter
using least-squares non-linear fitting for the description of all the
experimental results obtained in their study, having a value of
1.94.
The values for volumetricpower consumptioncalculatedby this
empirical correlation and the experimentally measured values fit
within a deviation range that does not exceed 30%. In the range
0.01 to 0.2 kW m3, with shaking frequency from 80 to 380 min1,
filling volumes of 4% to 20% of nominal flask volume and
shaking diameter from 2.5 to 5 cm, larger discrepancies are found
between calculated and measured values. The corresponding
data was gathered at low shaking frequency (80 to 120 min1)
and, therefore, at low Reynolds numbers (Re 500 to 5000),
possibly within the transition from laminar to turbulent flow, a
feature that could account for the increased deviation between
predicted and experimental values.
The discrepancy between experimental and predicted data at
low power consumption was overcome in liquids with viscosities
between 0.8 and200 mPa s,105 where a correlation was found that
took into consideration all the flow regimes:
Ne = 70Re1 + 25Re0.6 + 1.5Re0.2 (24)
This correlationconsists of a laminar (Re1), a transition (Re0.6),
and a turbulent term (Re0.2). From the power number variation
with the flask Reynolds number, two flow conditions were
identified: in-phase conditions, where the bulk of the liquid
in the flask circulates in phase with the shaking platform; and
out-of-phase conditions, where only a minor fraction of the
liquid is actually moving along the flask wall.67 The out-of-phase
conditions lead to a decrease in volumetric power consumption,
mixing gas/liquid mass transfer. In order to systematically describethe in-phase and out-of-phase conditions, a new non-dimensional
number, called the phase number (Ph), was derived based on an
analogy to a partially filled, rotating horizontal drum, and can be
expressed as
Ph =d0
d
1+ 3log10
(2N)
d2
4
1
14
V0.33
d
2
2
(25)
Buchs etal.98 established that all operating conditions where
Ph > 1.26arein-phasewhileout-of-phaseconditionsareobserved
for Ph < 1.26, which are prone to occur when large flasks or high
viscosityfluids are used.11 Nonetheless, out-of-phase conditions in
largeflasks at water-likeviscosities arepossibleif theflask is quickly
accelerated.106 This may occur, if (i) the shaking machine has a
strong engine, (ii) the load of the machine is low (small number of
flasks placed on the shaker table or (iii) the shaking flasks which
wereremovedfromtheshakingtable(e.g.forsampling)areplaced
back on the running machine.
This phenomenon of out-of-phase operating conditionsmay be
of great practical relevance, since working under such conditions
will significantly reduce the oxygen transfer and mixing intensity,having a strong impact on strain and medium development. The
flow in a shaking flask tends to be in-phase at large shaking
diameter, low viscosity, large filling volume, higher shaking
frequency and small number and size of baffles.
Kato etal.107 used a calorimetric method, based on the method
developed by Sumino etal.,108 for assessing power consumption
in larger shaken flasks (nominal volume up to 20 L). Despite the
increase in volume, the order of magnitude ofP/V is the same as
for smaller scale shaking flasks, up to a nominal volume of 2 L and
having different geometries.104
Similar studies have been conducted reporting a stronger
dependency between power consumption and shaking speed,
P N.5.75 Nonetheless, a narrower range of shaking frequencies,
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between 100 and 200 rpm was used, compared with the
100 300 rpm range of Kato etal.1 This may also account for
the volumetric power consumption reported in either work, from
less than 2 kW m3 to 5 kW m3, respectively. Therefore, it can be
concluded that the increase in power consumption is much more
pronounced in the region of low shaking frequencies, between
100 and 200 rpm.
Raval etal.109 compared the torque method and temperature
methodforthedeterminationofpowerconsumptionindisposable
shaken bioreactors of 2 L polycarbonate (PC) bottles and 20 L
polypropylene (PP). Data points collected by both methods were
within30%tolerance range.Values of3.5 kW m3 wereobtained
in 2 L flasks with filling volume of 250 mL at 300 rpm (shaking
diameter 50 mm).
Another approach for estimation of the volumetric power
consumption was proposed by Zhang etal.103 Using CFD
techniques,theseauthorswereabletopredictpowerconsumption
when 250 mL shake flasks were operated between 100 and
300 rpm, with shaking diameters between 20 and 60 mm and
filling volumes between 25 and 100 mL. CFD models suggest that
P/V can be correlated with the filling volume or with the shaking
frequency according to P/V V0.7
and P/V N2.7
, respectively.Both correlationsare in agreementwith those suggestedby Buchs
etal.104 Nonetheless, for lower shaking diameters the exponent
in the shaking frequency correlation decreased to 1.6, suggesting
that the applicability of these correlationsare limited to a range of
amplitudes. Values predicted were between 40 and 1200 W m3.
The powerconsumptionestimates werefoundto be moresensitive
to changes in shaking amplitude than to frequency
Multi-well plates
Despite the widespread application of MWPs, currently there is
no experimental report on power consumption in these devices,
mainlyduetolackofcommercialtorquemetersorothermeasuring
methods withsufficient sensitivity to perform suchmeasurements.In order to overcome this situation, Zhang etal.8 proposed the use
of CFD to obtain estimates of power consumption. These authors
applied the methodology followed by Zhang etal.103 where the
local energy dissipation rate was obtained using
=v
(26)
where V is the viscous dissipation term. The power consumption
based on the fluid friction is calculated from
P
V
=
V0
vdV
V
(27)
where V, can be expressed in terms of shear rates:103
V = 2
u
x
2+
v
y
2+
w
z
2+
u
y+
v
x
2
+
v
z+
w
y
2+
u
z+
w
x
2(28)
where U(u,v,w) is the velocity vector(velocity component) andx(x,
y, z) is the moving grid spatial vector (spatial component).
The results showed that power consumption and energy
dissipation rates in the shaken microwells are strongly affected
by the size of the well and the filling volume, as well as by the
shaking frequency and amplitude. These effects are higher in 96-
well microtiter plates than in 24-well microtiter plates under the
same operating conditions.
Moreover, two situations can be distinguished:
1. The power consumption in the 24-well reactor does not
increase linearly as theshaking frequency is increasedat 3 mm
shaking diameter. Up to roughly 800 rpm, there is a decreasein power consumption, presumably due to out-of-phase
conditions. The estimated volumetric power consumption
is more sensitive to changes in shaking amplitude than to
frequency.
2. The volumetric power consumption at orbital shaking ampli-
tudes of both 3 mmand 6 mmincreased linearly with increase
in shaking frequency. Increasing the shaking amplitude from
3 mm to 6 mm, led to an increase in the volumetric power
consumption of 1000 2000 W m3 using shaking frequencies
in the range of 800 1000 rpm.
The volumetric power consumption was compared for a 24-well
microtiter plate, 96-well microtiter plate, 20 L stirred reactor, 6 mL
miniature stirred reactor110 and a 250 mL shake flask102 at feasibleoperating conditions.
The miniature stirred reactor closely matched the configuration
of conventional stirred reactors, only scaled down to 6 mL
scale.11 The P/V was similar in all reactors with the exception
of shaken flasks and the 24-well microtiter plates. The values used
for microtiter plates were obtained by CFD studies in specific
conditions; nonetheless similar values of P/V can be reached in
shaken systems.
Case studies: scale-up from shaken devices and miniaturestirredreactorsbasedin specificpowerconsumptionsimilarity
Aqueous systems
Despite the large number of studies on scale-up of fermentationprocesses andsome on bioconversion processes, examples on the
use of volumetric power consumption as key parameterare scarce.
Gill etal.7 developed a prototype of a microreactor that enables
parallel operation of 4 16 independently controlled experiments.
Each microreactorhas a maximum working volumeof 100 mL and
is equipped with a magnetically driven six-blade Rushton turbine,
with a stirring range of 100 2000 rpm. Growth ofE. coli TOP10
pQR239was scaled-upfromthismicroreactor toa 2 L reactor fitted
with two six-blade Rushton turbine impellers111 using as constant
the power consumption. P/V values used in this study were 657,
1487 and 2960 W m3.
At the lowest P/V value of 657 W m3, the 2 L reactor signif-
icantly underperforms compared with the miniature bioreactor,achieving a final biomass concentration of almost 3 g L1 less
(Xfinal in the miniature bioreactor was 5.6 g L1). This is likely to be
the result of operating at a reduced agitation rate, and the poor
gasliquid dispersion that was observed at the 2 L scale under
these operating conditions. Given the poor oxygen transfer at the
2 L scale, the dissolved oxygen tension reached zero much earlier,
and cell growth was clearly seen to become oxygen limited. The
performance of the 2 L reactor was improved at higher P/Vvalues
(>1000 W m3), with very similar max and final biomass con-
centration values obtained at both scales. The trends for oxygen
depletion during the exponential growth phase and for the time
taken forbothsystems tobecome oxygenlimited were similar and
reproducible at the twohigher P/Vvalues(1487and 2960 W m3).
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The volumetric power consumption was also used to scale-up
the alginate production using Azotobacter vinelandii cells, from
500 mL shake flasks to 14 L reactor.112 The study showed that
when an initial power draw of 0.27 kW m3 was applied, a specific
growth rate of 0.16 h1 was obtained in a stirred reactor, which
roughly doubled the specific growth rate obtained in shake flasks
(0.09 h1). Moreover, differences in the broth viscosity, concentra-
tion profiles and molecular weight of the alginate were observed.
In order to overcome these, the initial P/V in the reactor or along
the time course of the cultivation was reduced, which ultimately
allowed oneto match the molecularcharacteristics of the alginate
obtained in shake flasks. This approach further highlights the
potential limitations of shaken vessels as starting platforms for
scaling-up when significant modifications in medium rheology
take place throughout the process. This study was based on the
theoretical analysis of power consumption in shake flasks. The
power consumption in shake flasks was estimated from extrapo-
lationof data reported by Buchs etal.104,105This is a key feature, as
thechangesin power inputaffect theOTR,which in turn affects the
molecular characteristics of alginate. Further work was performed
in order to gain insight into the power consumption along cell
growth for the same alginate-producing system. Pena etal.113
showed that the power consumption increased exponentially
during fermentation, achieving a maximum value of 1.4 kW m3
after 40 h cultivation. This increase was due to the increased
viscosity of the culture broth, which resulted from the increase
in the molecular mass of alginate and polymer concentration. In
this period, a maximal alginate concentration of 5 kg m3, with a
maximum molecular weight of 550 kDa was obtained.
Although the viscosity increasedin theperiod from 40 to 70 h, a
slight drop in the power consumption was observed, leading to a
value of 1.2 kW m3 at 70 h cultivation. This behavior waspossibly
due to out-of-phase conditions, which could also account for the
results obtained previously by Reyes etal.112
Pena etal.114 tried toreproduce themean molecularmassof the
alginates obtained in shake flasks, in a stirred reactor maintainingP/V constant. A 500 mL Erlenmeyer flask was used, containing
1/5 filling volume. The power consumption during alginate pro-
duction increased exponentially from 0.18 to 1.4 kW m3 during
the first 40 h of culture and remained practically constant during
the rest of the fermentation. The exponential profile of the power
consumption(from0.2to1.2 kW m3)wassimulatedalongthefer-
mentationina14 Lbenchreactor,containing10 LofBurkmedium,
by adequately controlling the agitation rate from 250 to 515 rpm.
Further dissemination of the evaluation of the validity of
constant P/V as criterion for scaling-up is dependent on the
availability of methodologies and tools for easily assessing this
parameter in miniaturized devices.
Studies in two-phasesystems
All the above examples are for aqueous systems. When substrates
that have low water solubility are involved, two-liquid phase
systems can be used. In these cases, P/V is particularly important
as drop diameter (and hence the interfacial area available for
mass transfer between phases) depends on the maximum energy
dissipation rate or volumetric power consumption. Moreover, for
efficient extraction it determines also the mean drop size and the
dispersion of the immiscible organic phase.115
In a stirred vessel dmax (maximum drop diameter) will be given
bydmax
T
We0.6T (29)
and
WeT =cN
2T3
(30)
where WeT is thestirred-tankWeber number and istheinterfacial
tension.116 To account for the effect of volume fraction on dmax, a
linear concentrationcorrection functionwiththe followinggeneral
form was used:
dmax
T= c1(1+ c2)We
0.6T (31)
where c1 and c2 are constants and is the volume fraction of
the dispersed phase.61 The constant c2 is considered equal to 3
when it accounts for turbulence damping at low dispersed-phase
concentrations, or higher than 3 for coalescing systems.117
The maximum drop diameter is also a key parameter since it is
generally considered proportional to the Sauter mean diameter
d32, although this has been questioned.118 The Sauter mean
diameter, commonly used in processes depending on interfacial
area, is defined as the ratio of the third to the second moment of
the drop size distribution:
d32 =
ki=1
nid3i
ki=1
nid2i
(32)
where kis the number of size classes, ni the number of drops and
di the diameter of drops in size class i.117119
These aforementioned equations predict an increase in drop
size with increasing dispersed phase volume fraction, up to
about 40%. At higher fractions (usually above 50%), a further
increasein thedispersedphase concentrationresultsin decreasing
drop size. This behavior is attributed to a change in the dropbreakage mechanism, from turbulent eddy at low concentrations,
to boundary layer at high concentrations.117,120
BuchsandZoels120 showedthatshakeflasksledtolowerlevelsof
hydro-mechanical stress, as power consumption was much more
evenly distributed than in stirred tanks. This is due to different
mixing mechanism present in either reactor. Thus, in stirred tank
reactors, the power drawn from the region close to the stirrer is
quite high comparedwith the average P/V,sinceasmallimpelleris
used to promote mixingin a large vessel. a relatively small impeller
agitates a relatively bulky tank, leading to higher power drawn
in the region adjacent to the stirrer compared to the measured
average or specific P/V. Onthe other hand, whenshakenflasks are
used, power is more homogeneously distributed throughout thevessel, since energy is introduced through a relatively large wall
area.121 These effects must be taken also into account if cultures
are used where shear stress influences physiological behavior,
such as filamentous organisms.
Cull etal.116 exploited the use of two-phase systems for
the whole-cell bioconversion of 1,3-dicyanobenzene (1,3-DCB)
to 3-cyanobenzamide.with resting cells of Rhodococcus R312.
Volumetric power consumption (or N3Di2 constant) and constant
tip speed (or NDi constant) were the two criteria tested for scale-
up, from a 3 L to a 75 L reactor. The system was composed
of a phosphate buffer phase, where the cells were dispersed,
and toluene, which contained 1,3-DCB and, throughout the
bioconversion, the 3-cyanobenzamide formed.
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Sauter mean drop diameters and drop size distributions were
verysimilarforscale-uponthebasisofP/V, in geometrically similar
reactors. In all cases the drop size distributions obtained were log-
normal. The results presented in that work were obtained in
a specific phase system comprising 20% v/v toluene dispersed
in an aqueous buffer containing up to 10 gcell wet weight L1
of Rhodococcus R312 cells. Despite being system specific, this
work contributed to establish specific power consumption as a
suitable tool for scale-up of two-phase bioconversion systems.
Moreover, it is demonstrated that a scale increase of 25-fold is
possible maintaining system specificity. The use of smaller reactors
leads to cost reduction with reagents and overall process power
consumption, among others. Moreover, problems that might be
encountered at the large scale can be rapidly and efficiently
identified in smaller scale.
Another example of scale-up of a two-phase system based on
the volumetric power consumption is the production 6-pentyl-
-pyrone (6PP) performed by cells of Trichoderma harzianum.
Rocha-Valadez etal.121 reported a 20-fold scale-up, from 500 mL
shake flasks to a 10 L stirred tank reactor. 6PP production
followed a sigmoid-shaped relationship with P/V, regardless of
the production scale or impeller diameter. Synthesis of 6PP wastriggered earlier in the stirred reactor, suggesting a physiological
response mechanism of T. harzianum towards hydrodynamic
stress. Overall, at low P/V values (from 0.08 to 0.4 kW m3) a
gradual increase in P/V improved 6PP production; however, for
P/V > 0.6 kW m3, 6PP concentration was significantly reduced
due to higher hydrodynamic stress.
P/Vshiftinfluenced microbialgrowth in the stirred reactor since
the specific growth rate decreased from 0.052 h1 at 0.08 kWm3
to 0.033 h1 at 1.6 kWm3. On the other hand the specific growth
rate was practically unaffected by P/V in the shake flask system.
Higher shear rates involve drastic physiological changes including
cellular differentiation and conidiospore production. This work
showed thatphysiological changes observedduring process scale-
up (i.e. microbial growth, production rates and sporulation) weretriggeredas resultof differences in the shear conditions prevailing
in the two systems employed.
P/V provides a suitable scale-up criterion from miniaturized
devices when two-phase systems are involved. Further studies
would be welcome addressing particular cases where MWP are
used as the starting platforms.
OTHER SCALE-UP PARAMETERSExamplesoftheapplicationofotherscale-upparametersarescarce
due to the fact that both kLa and P/V incorporate information
contained in the Reynolds number and mixing time, among
others. Nonetheless, examples of such criteria are given.
Constant impeller tip speed
The impeller tip speed, vtip, is expressed as
vtip = NT (33)
Tip speed is used as a rule for scale-up when the relationship
between shear and morphology is far from well understood, as
happens in mycelial cultures.122 A rough rule of thumb suggests
that cell damage can occur at tip speeds above 3.2 m s1, but
the exact value is influenced by many factors such as broth
rheology. Calculated tip speeds are usually greater than 3 m s1
for production scale reactors.122 Although useful for estimating
the potential for hyphae breakage and thus alteration of broth
morphology when branched yeast, filamentous bacterial and
fungal fermentations are involved, tip speed is less useful for
single cell bacterial or yeast fermentations. If scale-up is carried
out using constant tip speed (with geometric similarity), then the
value ofP/V is often lowered, which can adversely affect aeration
efficiency. It is possible to overcome this drawback by using more
impellers in the larger vessel in such a way that both tip speed and
P/Vare kept constant. Tip speed influences impeller shear, which
is proportional to the product of impeller tip speed and impeller
diameter, NDi2, for turbulent flow conditions.122
Hiruta etal.123 demonstrated that maintaining impeller tip
speed of 270 m min1 allowed scaling-up the production of -
linolenic acid by Mortierella ramanniana mutant MM 15-1 from a
30 L to a 1 m3 reactor.
More recently, Dubey etal.124 scaled-up the demethylation
of colchicine and their derivatives using Bacillus megaterium
ACBT03 cells, from a 5 L to a 70 L reactor. Under optimum culture
conditions the key monitoring factors to scale-up the process of
demethylation were aeration rate of 2.5 vvm and impeller tip
velocity of 4710 cm min1
.
Similar Reynolds number
Reynolds number is expressed as:
Re =TN2
(34)
The use of constant Reynolds number is hardly ever used
for fermentation scale-up, since the effect of aeration on the
process is notincorporated,125 andthe Reynoldsnumber generally
increases for successful scale-up designs. Other dimensionless
groups have also been examined for scale-up with limited
success, often resulting in technically unrealistic equipment andoperatingparameters. As it is difficultto maintain all dimensionless
parameters constant upon scale-up, those most important to the
process must be identified accurately.122
Constant mixing time
The mixing time tm denotes the time required for the reactor
composition to achieve a specified levelof homogeneity following
additionof a tracerpulse at a singlepointin thevessel. Mixingtime
containsinformation about flowand mixing within the reactorand
can be useful forbiosynthesis processes scale-up. Themixing time
tm is defined as1
tm =V
NfNT3
(35)
where Nf is the pumping number. The mixing time is typically
measured in stirred vessels. Nonetheless, there is an increased
interest in determining this parameter in shaken reactors. Gerson
etal.126 used a mixing probe to determine fluid mixing in a 1 L
shaken flask with filling volume of 540 mL at different shaking
frequencies. The results demonstrated that it is possible to
make such measurements, and that the mixing intensity rises
monotonically with shaking frequency in both stirred reactors and
shake flasks. Also, the range of mixing intensities measured by the
device is similar in both systems over the range studied.
Recently, Nealon etal.127 developed a high-speed video
technique for the accurate quantification of jet macro-mixing
times in static microwell plates, which also enables visualisation
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of jet formation and liquid flow patterns within the wells. Three
microwell geometries were investigated: a single well from a
standard 96-round well plate and dimension modified 96-well
plate. A general correlation was found for the time to reach 95%
homogeneity (s):
t95 =2.60D1.5h0.5
u0dn(36)
where dn is the nozzle diameter, D is the well or vessel diameter, his the liquid height and u0 is the nozzle velocity.
CONCLUSIONSDespite the relevance of the scale-up issue in biotechnology,there
is no straightforward and uniform strategy to tackle this matter.
A suitable scale-up criterion is elaborated in accordance with the
individual product, process and the facility.
An overall scale-up strategy consists of (i) a comprehensive
and detailed process characterization, and (ii) an appropriate
process control and process design. Owing to the complex
nature of bioprocesses (biotransformation, bioconversion and
fermentation) successful scale-up in most cases will not be basedon a straightforward strategy, but rather is the outcome of an
independent optimization on each process scale. Nonetheless,
bioconversions and fermentations are tentatively scaled-up on
the basis of kLa or volumetric power consumption from lab- to
pilot-scale. With the increasing ability to incorporate in MWPs and
in miniature and microreactors devices that allow the monitoring
of key process variables, such as dissolved oxygen tension,
pH, optical density or protein production, the application of
such small scale reactors is gaining widespread use in process
optimization, rather than just in the early stages of screening.
This pattern, that places small scale reactors in later stages of
process development, puts more focus on the need for increasing
the accuracy of scaling criteria. This has clearly been taken into
consideration, as shown by the number of papers dedicatedto this matter that have been published recently. Accordingly
the number of case studies reporting the successful scaling
up from MWPs and similar devices to bench scale reactor
or above is increasing. The insight required to obtain more
knowledge on this matter has received significant contributions
from the developments in image analysis, data processing and
development of predictive models, namely through the use
of CFD. In spite of the many existing studies, no examples of
direct scale translation to industrial scale exist. There is a strong
likelihood that scaling from shaken vessels to plant scale will
not become a reality, given distinct hydrodynamic environments,
preventing fullreproducibility, hencecompromisingthe outcome.
The translation from miniaturized to production environment is
nevertheless possible by scaling-out/numbering-up rather than
scaling-up. In this approach, large numbers of microreactors,
operating in continuous mode, are assembled so that production
up to tons/year basis can be achieved.
ACKNOWLEDGEMENTSMPC Marques and P Fernandes thank Fundacao para a Ciencia
e Tecnologia (Portugal) for financial support in the form of a
PhD grant SFRH/BD/24433/2005 and programme Ciencia 2007,
respectively. This work was partially funded by research project
POCI/SAU-MMO/59370/2004 from Fundacao para a Ciencia e a
Tecnologia (Portugal).
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